221. Maximal Square

dp function的含义比较特别，dp[i][j] stands for the max square side length whose lower right corner is matrix[i][j].
转换方程也很棒，以matrix[i][j]为右下角的正方形边长是以matrix[i - 1][j], matrix[i][j - 1], matrix[i - 1][j - 1]最小值加一，搞清楚这个关键点问题就很简单了。

class Solution {
    public int maximalSquare(char[][] matrix) {
        if (matrix == null || matrix.length == 0 || matrix[0].length == 0){
            return 0;
        }
        int m = matrix.length;
        int n = matrix[0].length;
        //dp[i][j] representing max square side length whose lower-right corner is matrix[i][j]
        int[][] dp = new int[m][n];
        int max = 0;
        for (int i = 0; i < m; i++){
            dp[i][0] = matrix[i][0] - '0';
            max = Math.max(max, dp[i][0]);
        }
        for (int i = 0; i < n; i++){
            dp[0][i] = matrix[0][i] - '0';
            max = Math.max(max, dp[0][i]);
        }
        for (int i = 1; i < m; i++){
            for (int j = 1; j < n; j++){
                if (matrix[i][j] == '1'){
                    dp[i][j] = Math.min(dp[i - 1][j], Math.min(dp[i][j - 1], dp[i - 1][j - 1])) + 1;
                } else {
                    dp[i][j] = 0;
                }
                max = Math.max(max, dp[i][j]);
            }
        }
        return max*max;
    }
}